As for going to NUS or KCL, I think it depends on what you want to do.
You might want to think about this: Compare Singapore's population and the number of universities it has, and then compare UK's population and the number of Universities it has.
Sure, there's Oxbridge, Warwick, LSE, but what's the proportion of UK home students who enter? Now compare this proportion with NUS.
Everyone wants to go to "the best Universities". But it's not that easy, surprisingly.
KCL is decent. It's not the absolute best - but as long as you do well in your studies, and have decent student participation / internships / core-curricular activities, you'll not have problems getting a job in UK, or even in SG.
What about post grad? Well, you'll need to show that you have sufficient knowledge of your field at undergraduate level - that concerns the modules you take then at KCL / NUS. You probably won't take many mathematics or economics modules in KCL / NUS for the courses you're contemplating. So that's something to think about.
I'd say go for KCL, *unless* you are the sort that stays at home / are mugger toad / hangs out with people of same nationality / etc. Why? Being in another country -> lots of opportunities to do something you can never do in SG. Furthermore, the more extra stuff (this can range from exploring Europe, climbing mountains, etc - so not necessarily academic or job related) you do, it's something additional you can write on your CV (if you are so inclined), can win awards geared to international students / home students, and more. Plus it's something which SG can't offer (cheaply at least).